Vertices A, B, C and D of a quadrilateral ABCD lie on a circle. ∠A is three times ∠C and ∠D is two times ∠B. What is the difference between the measures of ∠D and ∠C?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 75°.
Let's assume the ∠C = x and ∠B = y
So, ∠A = 3x and ∠D = 2y
The sum of opposite angles of a cyclic quadrilateral is 180°
∠A + ∠C = 180°
⇒ 3x + x = 180°
⇒ x = 45°
∠B + ∠D = 180°
⇒ y + 2y = 180°
⇒ y = 60°
∠D - ∠C = 2 × 60° - 45° = 75°